New Polynomials and Numbers Associated with Fractional Poisson Probability Distribution
Nick Laskin
TL;DR
This paper introduces new polynomials and numbers linked to the fractional Poisson distribution, expanding classical combinatorial sequences and their generating functions.
Contribution
It presents novel generalizations of Bell polynomials, Bell numbers, and Stirling numbers related to fractional Poisson probability.
Findings
Derived new generating functions for the generalized sequences
Established connections between fractional Poisson distribution and combinatorial numbers
Extended classical combinatorial concepts to fractional settings
Abstract
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
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